Pierre Vallois

Quelques approximations du temps local brownien (2008)

We give some approximations of the local time process $(L_t^x)_{t\geqslant 0}$ at level $x$ of the real Brownian motion $(X_t)$. We prove that $ \frac{2}{\epsilon}\int_0^{t} X_{(u+\epsilon)\wedge...

Identification of Pharmacokinetics Models in the presence of Timing Noise (2008)

We give some approximations of the local time process $(L_t^x)_{t\geqslant 0}$ at level $x$ of the real Brownian motion $(X_t)$. We prove that $ \frac{2}{\epsilon}\int_0^{t} X_{(u+\epsilon)\wedge...

Bastogne, Thierry, Mézières-Wantz, Sophie, Ramdani, Nacim, Vallois, Pierre, Barberi-Heyob, Muriel

The problem addressed in this paper deals with the parameter estimation of in vitro uptake kinetics of drugs into living cells in presence of timing noise. Effects of the timing noise on the bias and...

Identification of Pharmacokinetics Models in the presence of Timing Noise (2008)

Bastogne, Thierry, Mézières-Wantz, Sophie, Ramdani, Nacim, Vallois, Pierre, Barberi-Heyob, Muriel

The problem addressed in this paper deals with the parameter estimation of in vitro uptake kinetics of drugs into living cells in presence of timing noise. Effects of the timing noise on the bias and...

Convergence at first and second order of some approximations of stochastic integrals (2008)

Bérard-Bergery, Blandine, Vallois, Pierre

We consider the convergence of the approximation schemes related to Itô's integral and quadratic variation, which have been developed in [8]. First, we prove that the convergence in the a.s. sense...

A family of generalized gamma convoluted variables (2008)

Convergence at first and second order of some approximations of stochastic integrals (2008)

This paper consists of three parts: in the first part, we describe a family of generalized gamma convoluted (abbreviated as GGC) variables. In the second part, we use this description toprove that...

Bérard-Bergery, Blandine, Vallois, Pierre

We consider the convergence of the approximation schemes related to Itô's integral and quadratic variation, which have been developed in [8]. First, we prove that the convergence in the a.s. sense...

A family of generalized gamma convoluted variables (2008)

On subexponentiality of the Lévy measure of the diffusion inverse local time; with applications to penalizations (2008)

This paper consists of three parts: in the first part, we describe a family of generalized gamma convoluted (abbreviated as GGC) variables. In the second part, we use this description toprove that...

On subexponentiality of the Lévy measure of the diffusion inverse local time; with applications to penalizations (2008)

For a recurrent linear diffusion on $\Bbb R_+$ we study the asymptotics of the distribution of its local time at $0$ as the time parameter tends to infinity. Under the assumption that the Lévy...

On subexponentiality of the L\'evy measure of the diffusion inverse local time; with applications to penalizations (2008)

For a recurrent linear diffusion on $\Bbb R_+$ we study the asymptotics of the distribution of its local time at $0$ as the time parameter tends to infinity. Under the assumption that the Lévy...

Penalisation of Brownian motion with its maximum and minimum processes as weak forms of Skorokhod embedding, X (2008)

For a recurrent linear diffusion on $\R_+$ we study the asymptotics of the distribution of its local time at 0 as the time parameter tends to infinity. Under the assumption that the L\'evy measure of...

Penalisation of Brownian motion with its maximum and minimum processes as weak forms of Skorokhod embedding, X (2008)

We develop a Brownian penalisation procedure related to weight processes $(F_t$) of the type : $F_t := f(I_t, S_t) where $f$ is a bounded function with compact support and $S_t (resp. I_t)$ is the...

Limiting laws associated with Brownian motion perturbed by its maximum, minimum and local time II (2007)

We develop a Brownian penalisation procedure related to weight processes $(F_t$) of the type : $F_t := f(I_t, S_t) where $f$ is a bounded function with compact support and $S_t (resp. I_t)$ is the...

Limiting laws associated with Brownian motion perturbed by its maximum, minimum and local time II (2007)

We obtain probability measures on the canonical space penalizing the Wiener measure by a function of its maximum (resp. minimum, local time). We study the law of the canonical process under these new...

Approximation via regularization of the local time of semimartingales and Brownian motion (2007)

We obtain probability measures on the canonical space penalizing the Wiener measure by a function of its maximum (resp. minimum, local time). We study the law of the canonical process under these new...

Approximation via regularization of the local time of semimartingales and Brownian motion (2007)

Through a regularization procedure, few approximation schemes of the local time of a large class of one dimensional processes are given. We mainly consider the local time of continuous...

Parameter estimation of pharmacokinetics models in the presence of timing noise (2007)

Through a regularization procedure, few approximation schemes of the local time of a large class of one dimensional processes are given. We mainly consider the local time of continuous...

Bastogne, Thierry, Mézières-Wantz, Sophie, Ramdani, Nacim, Vallois, Pierre, Barberi-Heyob, Muriel

We consider a model of pharmacokinetics which takes into account the presence of timing noise

Approximation via regularization of the local time of semimartingales and Brownian motion (2007)

Bergery, Blandine Berard, Vallois, Pierre

Through a regularization procedure, few approximation schemes of the local time of a large class of one dimensional processes are given. We mainly consider the local time of continuous...

Parameter estimation of pharmacokinetics models in the presence of timing noise (2007)

Bastogne, Thierry, Mézières-Wantz, Sophie, Ramdani, Nacim, Vallois, Pierre, Barberi-Heyob, Muriel

We consider a model of pharmacokinetics which takes into account the presence of timing noise

Statistical and renewal results for the random sequential absorption model applied to a unidirectional multicracking problem (2007)

Calka, Pierre, Mézin, André, Vallois, Pierre

We model the positions of multiple cracks via a stationary process which is a particular of the RSA process.

Statistical and renewal results for the random sequential absorption model applied to a unidirectional multicracking problem (2007)

Calka, Pierre, Mézin, André, Vallois, Pierre

We model the positions of multiple cracks via a stationary process which is a particular of the RSA process.

Elements of Stochastic Calculus via Regularisation (2007)

Limiting laws for long Brownian Bridges perturbed by their one-sided maximum, III (2007)

This paper first summarizes the foundations of stochastic calculus via regularization and constructs through this procedure Itô and Stratonovich integrals. In the second part, a survey and new...

Limiting laws associated with Brownian motion perturbated by normalized exponential weights I. (2007)

Limiting laws for long Brownian Bridges perturbed by their one-sided maximum

m-order integrals and generalized Ito's formula; the case of a fractional Brownian motion with any Hurst index (2007)

We determine the rate of decay of the expectation Z(t) of some multiplicative functional related to Brownian motion up to time t. This permits to prove that the Wiener measure, penalized by this...

Gradinaru, Mihai, Nourdin, Ivan, Russo, Francesco, Vallois, Pierre

Given an integer m, a probability measure ν on [0,1], a process X and a real function g, we define the m-order ν-integral having as integrator X and as integrand g(X). In the case of the...

Approximation of the distribution of the supremum of a centered random walk. Application to the local score. (2007)

Etienne, Marie Pierre, Vallois, Pierre

We determine the rate of convergence of the distribution function of the one-sided supremum of a centered random walk to its limit.

On first range times of linear diffusions (2007)

Limiting laws associated with Brownian motion perturbated by normalized exponential weights I. (2007)

We consider first range times (with randomized range level) of linear diffusions

On first range times of linear diffusions (2007)

We determine the rate of decay of the expectation Z(t) of some multiplicative functional related to Brownian motion up to time t. This permits to prove that the Wiener measure, penalized by this...

Limiting laws for long Brownian Bridges perturbed by their one-sided maximum, III (2007)

We consider first range times (with randomized range level) of linear diffusions

m-order integrals and generalized Ito's formula; the case of a fractional Brownian motion with any Hurst index (2007)

Limiting laws for long Brownian Bridges perturbed by their one-sided maximum

Gradinaru, Mihai, Nourdin, Ivan, Russo, Francesco, Vallois, Pierre

Given an integer m, a probability measure ν on [0,1], a process X and a real function g, we define the m-order ν-integral having as integrator X and as integrand g(X). In the case of the...

Approximation of the distribution of the supremum of a centered random walk. Application to the local score. (2007)

Etienne, Marie Pierre, Vallois, Pierre

We determine the rate of convergence of the distribution function of the one-sided supremum of a centered random walk to its limit.

Quelques approximations du temps local brownien (2007)

On maximum increase and decrease of Brownian motion (2007)

We give some approximations of the local time process $(L_t^x)_{t\geqslant 0}$ at level $x$ of the real Brownian motion $(X_t)$. We prove that $ \frac{1}{\epsilon}\int_0^t ( \indi_{\{ x

On the excursion theory for linear diffusions (2007)

The joint distribution of maximum increase and decrease for Brownian motion up to an independent exponential time is computed. This is achieved by decomposing the Brownian path at the hitting times...

Salminen, Paavo, Vallois, Pierre, Yor, Marc

We present a number of important identities related to the excursion theory of linear diffusions. In particular, excursions straddling an independent exponential time are studied in detail. Letting...

Asymptotic behavior of the local score of independent and identically distributed random sequences (2007)

Daudin, Jean-Jacques, Vallois, Pierre, Etienne, Marie-Pierre

Asymptotic behavior of the local score via Brownian motion

Penalizing a BES(d) process (0 < d < 2) with a function of its local time, V (2007)

Some extensions of Pitman's and Ray-Knight's theorems for penalized Brownian motions and their local times, IV (2007)

We study the penalization of a BES(d) process (0

Donati-Martin, Catherine, Roynette, Bernard, Vallois, Pierre, Yor, Marc

We give some extensions of Pitman's and Ray-Knight's theorems via a penalization procedure involving Brownian motion and its local time at 0

We precise the choice of constants in computations related to Bessel processes with dimension d=2(1-alpha), 0 < alpha < 1

Range of Brownian motion with drift (2007)

Tanré, Etienne, Vallois, Pierre

We study the law of the range of Brownian motion with drift

Asymptotic behavior of the hitting time, overshoot and undershoot for some Lévy processes (2007)

Roynette, Bernard, Vallois, Pierre, Volpi, Agnès

We study the asymptotic behavior of the hitting time, overshoot and undershoot for some Lévy processes

Asymptotic behavior of the hitting time, overshoot and undershoot for some Lévy processes (2007)

Roynette, Bernard, Vallois, Pierre, Volpi, Agnès

We study the asymptotic behavior of the hitting time, overshoot and undershoot for some Lévy processes

On maximum increase and decrease of Brownian motion (2007)

On the excursion theory for linear diffusions (2007)

The joint distribution of maximum increase and decrease for Brownian motion up to an independent exponential time is computed. This is achieved by decomposing the Brownian path at the hitting times...

Salminen, Paavo, Vallois, Pierre, Yor, Marc

We present a number of important identities related to the excursion theory of linear diffusions. In particular, excursions straddling an independent exponential time are studied in detail. Letting...

Donati-Martin, Catherine, Roynette, Bernard, Vallois, Pierre, Yor, Marc

We precise the choice of constants in computations related to Bessel processes with dimension d=2(1-alpha), 0 < alpha < 1

Penalizing a BES(d) process (0 < d < 2) with a function of its local time, V (2007)

Some extensions of Pitman's and Ray-Knight's theorems for penalized Brownian motions and their local times, IV (2007)

We study the penalization of a BES(d) process (0

Range of Brownian motion with drift (2007)

We give some extensions of Pitman's and Ray-Knight's theorems via a penalization procedure involving Brownian motion and its local time at 0

Tanré, Etienne, Vallois, Pierre

We study the law of the range of Brownian motion with drift

Asymptotic behavior of the local score of independent and identically distributed random sequences (2007)

Daudin, Jean-Jacques, Vallois, Pierre, Etienne, Marie-Pierre

Asymptotic behavior of the local score via Brownian motion

Quelques approximations du temps local brownien (2007)

On maximum increase and decrease of Brownian motion (2007)

We give some approximations of the local time process $(L_t^x)_{t\geqslant 0}$ at level $x$ of the real Brownian motion $(X_t)$. We prove that $ \frac{1}{\epsilon}\int_0^t ( \indi_{\{ x

On the excursion theory for linear diffusions (2006)

Salminen, Paavo, Vallois, Pierre, Yor, Marc

We present a number of important identities related to the excursion theory of linear diffusions. In particular, excursions straddling an independent exponential time are studied in detail. Letting...

Quelques approximations du temps local brownien (2006)

Quelques approximations du temps local brownien (2006)

We give some approximations of the local time process $(L_t^x)_{t\geqslant 0}$ at level $x$ of the real Brownian motion $(X_t)$. We prove that $ \frac{1}{\epsilon}\int_0^t ( \indi_{\{ x

Quelques approximations du temps local brownien (2006)

We give some approximations of the local time process $(L_t^x)_{t\geqslant 0}$ at level $x$ of the real Brownian motion $(X_t)$. We prove that $ \frac{1}{\epsilon}\int_0^t ( \indi_{\{ x

Bergery, Blandine Berard, Vallois, Pierre

We give some approximations of the local time process $(L_t^x)_{t\geqslant 0}$ at level $x$ of the real Brownian motion $(X_t)$. We prove that $ \frac{2}{\epsilon}\int_0^{t} X_{(u+\epsilon)\wedge...

Generalized covariations, local time and Stratonovich Itô's formula for fractional Brownian motion with Hurst index H>=1/4 (2006)

Gradinaru, Mihai, Russo, Francesco, Vallois, Pierre

Given a locally bounded real function g, we examine the existence of a 4-covariation $[g(B^H), B^H, B^H, B^H]$, where $B^H$ is a fractional Brownian motion with a Hurst index $H \ge \tfrac{1}{4}$. We...

The laws of Brownian local time integrals (2006)

Gradinaru, Mihai, Roynette, Bernard, Vallois, Pierre, Yor, Marc

We obtain some identities in law and some limit theorems for integrals of the type $\int_{0}^{t}\varphi(s)d{\rm L}_{s}$. Here $\varphi$ is a positive locally bounded Borel function and ${\rm L}_{t}$...

Abel transform and integrals of Bessel local times (2006)

Gradinaru, Mihai, Roynette, Bernard, Vallois, Pierre, Yor, Marc

We study integrals of the type $\int_{0}^{t}\varphi(s)dL_{s}$, where $\varphi$ is a positive locally bounded Borel function and $L_{t}$ denotes the local time at level 0 of a Bessel process of...

The laws of Brownian local time integrals (2006)

Gradinaru, Mihai, Roynette, Bernard, Vallois, Pierre, Yor, Marc

We obtain some identities in law and some limit theorems for integrals of the type $\int_{0}^{t}\varphi(s)d{\rm L}_{s}$. Here $\varphi$ is a positive locally bounded Borel function and ${\rm L}_{t}$...

Generalized covariations, local time and Stratonovich Itô's formula for fractional Brownian motion with Hurst index H>=1/4 (2006)

Gradinaru, Mihai, Russo, Francesco, Vallois, Pierre

Given a locally bounded real function g, we examine the existence of a 4-covariation $[g(B^H), B^H, B^H, B^H]$, where $B^H$ is a fractional Brownian motion with a Hurst index $H \ge \tfrac{1}{4}$. We...

Abel transform and integrals of Bessel local times (2006)

Gradinaru, Mihai, Roynette, Bernard, Vallois, Pierre, Yor, Marc

We study integrals of the type $\int_{0}^{t}\varphi(s)dL_{s}$, where $\varphi$ is a positive locally bounded Borel function and $L_{t}$ denotes the local time at level 0 of a Bessel process of...

On maximum increase and decrease of Brownian motion (2006)

On maximum increase and decrease of Brownian motion (2006)

The joint distribution of maximum increase and decrease for Brownian motion up to an independent exponential time is computed. This is achieved by decomposing the Brownian path at the hitting times...

Elements of Stochastic Calculus via Regularisation (2006)

The joint distribution of maximum increase and decrease for Brownian motion up to an independent exponential time is computed. This is achieved by decomposing the Brownian path at the hitting times...

Elements of Stochastic Calculus via Regularisation (2006)

This paper first summarizes the foundations of stochastic calculus via regularization and constructs through this procedure It\^o and Stratonovich integrals. In the second part, a survey and new...

Elements of Stochastic Calculus via Regularisation (2006)

This paper first summarizes the foundations of stochastic calculus via regularization and constructs through this procedure Itô and Stratonovich integrals. In the second part, a survey and new...

On Maximum Increase and Decrease of Brownian Motion (2005)

This paper first summarizes the foundations of stochastic calculus via regularization and constructs through this procedure Itô and Stratonovich integrals. In the second part, a survey and new...

Limiting laws for long Brownian Bridges perturbed by their one-sided maximum, III (2005)

The joint distribution of maximum increase and decrease for Brownian motion up to an independent exponential time is computed. This is achieved by decomposing the Brownian path at the hitting times...

Limiting laws for long Brownian Bridges perturbed by their one-sided maximum, III (2005)

Limiting laws for long Brownian Bridges perturbed by their one-sided maximum

Limiting laws for long Brownian Bridges perturbed by their one-sided maximum, III (2005)

Limiting laws for long Brownian Bridges perturbed by their one-sided maximum

Limiting laws associated with Brownian motion perturbed by its maximum, minmum and local time II (2005)

Results of penalization of a one-dimensional Brownian motion $(X_t) $, by its one-sided maximum $\dis (S_t=\sup_{0 \leq u \leq t}X_u)$, which were recently obtained by the authors are improved with...

Limiting laws associated with Brownian motion perturbed by its maximum, minmum and local time II (2005)

We obtain probability measures on the canonical space penalizing the Wiener measure by a function of its maximum (resp. minimum, local time). We study the law of the canonical process under these new...

Limiting laws associated with Brownian motion perturbated by normalized exponential weights I (2005)

We obtain probability measures on the canonical space penalizing the Wiener measure by a function of its maximum (resp. minimum, local time). We study the law of the canonical process under these new...

Limiting laws associated with Brownian motion perturbed by its maximum, minmum and local time II (2005)

We determine the rate of decay of the expectation Z(t) of some multiplicative functional related to Brownian motion up to time t. This permits to prove that the Wiener measure, penalized by this...

Limiting laws associated with Brownian motion perturbated by normalized exponential weights I. (2005)

We obtain probability measures on the canonical space penalizing the Wiener measure by a function of its maximum (resp. minimum, local time). We study the law of the canonical process under these new...

Limiting laws associated with Brownian motion perturbated by normalized exponential weights I. (2005)

We determine the rate of decay of the expectation Z(t) of some multiplicative functional related to Brownian motion up to time t. This permits to prove that the Wiener measure, penalized by this...