Add to ORKGLet X be a d-dimensional diffusion process and M the running supremum of the first component. In this paper, in case of dimension d, we first show that for any t > 0, the law of the pair (M t , X t) admits a density with respect to Lebesgue measure. In uni-dimensional case, we compute this one. This allows us to show that for any t > 0, the pair formed by the random variable X t and the running supremum M t of X at time t can be characterized as a solution of a weakly valued-measure partial differential equation
Abstract. We consider a Lévy process Xt and the solution Yt of a stochastic differential equation d...
Abstract: Let ξ1 and ξ2 be two solutions of two stochastic differential equa-tions with respect to L...
AbstractLet X=(Xt,Ft)t⩾0 be a diffusion process on R given by dXt=μ(Xt)dt+σ(Xt)dBt,X0=x0, where B=(B...
Let X be a d-dimensional diffusion process and M the running supremum of the first component. In thi...
International audienceLet X be a d-dimensional diffusion and M the running supremum of its first com...
Let X be a continuous $d$-dimensional diffusion process and M the running supremum of the first comp...
International audienceLet X be a jump-diusion process and X * its running supremum. In this paper, w...
Consider a one dimensional diffusion process on the diffusion interval I originated in x0 ∈ I. Let a...
For processes $X(t),t>0$ governed by signed measures whose density is the fundamental solution of th...
In this paper, we develop a general methodology to prove weak uniqueness for stochastic differential...
We present a constructive probabilistic proof of the fact that if B = (Bt)t≥0 is standard Brownian m...
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Consider the Slepian process S defined by S(t) = B(t + 1) − B(t),t ∈ [0, 1] with B(t), t ∈ ℝ a stand...
summary:We solve the initial value problem for the diffusion induced by dyadic fractional derivative...
We show that simple diffusion processes are weak limits of piecewise continuous processes ...
Abstract. We consider a Lévy process Xt and the solution Yt of a stochastic differential equation d...
Abstract: Let ξ1 and ξ2 be two solutions of two stochastic differential equa-tions with respect to L...
AbstractLet X=(Xt,Ft)t⩾0 be a diffusion process on R given by dXt=μ(Xt)dt+σ(Xt)dBt,X0=x0, where B=(B...
Let X be a d-dimensional diffusion process and M the running supremum of the first component. In thi...
International audienceLet X be a d-dimensional diffusion and M the running supremum of its first com...
Let X be a continuous $d$-dimensional diffusion process and M the running supremum of the first comp...
International audienceLet X be a jump-diusion process and X * its running supremum. In this paper, w...
Consider a one dimensional diffusion process on the diffusion interval I originated in x0 ∈ I. Let a...
For processes $X(t),t>0$ governed by signed measures whose density is the fundamental solution of th...
In this paper, we develop a general methodology to prove weak uniqueness for stochastic differential...
We present a constructive probabilistic proof of the fact that if B = (Bt)t≥0 is standard Brownian m...
AbstractThe paper treats the problem of obtaining numerical solutions to the Fokker-Plank equation f...
Consider the Slepian process S defined by S(t) = B(t + 1) − B(t),t ∈ [0, 1] with B(t), t ∈ ℝ a stand...
summary:We solve the initial value problem for the diffusion induced by dyadic fractional derivative...
We show that simple diffusion processes are weak limits of piecewise continuous processes ...
Abstract. We consider a Lévy process Xt and the solution Yt of a stochastic differential equation d...
Abstract: Let ξ1 and ξ2 be two solutions of two stochastic differential equa-tions with respect to L...
AbstractLet X=(Xt,Ft)t⩾0 be a diffusion process on R given by dXt=μ(Xt)dt+σ(Xt)dBt,X0=x0, where B=(B...