Stability properties of constrained jump-diffusion processes.
Stationary distributions for jump processes with memory
We analyze a jump processes with a jump measure determined by a “memory” process . The state space of is the Cartesian product of the unit circle and the real line. We prove that the stationary distribution of is the product of the uniform probability measure and a Gaussian distribution.
Stochastic differential equations with jumps.
Stochastic FitzHugh-Nagumo equations on networks with impulsive noise.
Stochastic flow for SDEs with jumps and irregular drift term
We consider non-degenerate SDEs with a β-Hölder continuous and bounded drift term and driven by a Lévy noise L which is of α-stable type. If β > 1 - α/2 and α ∈ [1,2), we show pathwise uniqueness and existence of a stochastic flow. We follow the approach of [Priola, Osaka J. Math. 2012] improving the assumptions on the noise L. In our previous paper L was assumed to be non-degenerate, α-stable and symmetric. Here we can also recover relativistic and truncated stable processes and some classes...
Stochastic stability of neural networks with both Markovian jump parameters and continuously distributed delays.
Sur le passage de certaines marches aléatoires planes au-dessus d'une hyperbole équilatère
Symmetric jump processes : localization, heat kernels and convergence
We consider symmetric processes of pure jump type. We prove local estimates on the probability of exiting balls, the Hölder continuity of harmonic functions and of heat kernels, and convergence of a sequence of such processes.
Telegraph models of financial markets.
The classical limit of a class of quantum dynamical semigroups
The entrance boundary of the multiplicative coalescent.
The law of the hitting times to points by a stable Lev́y process with no negative jumps.
The martingale problem for a class of pseudo differential operators.
The principle of variation for relativistic quantum particles
The total continuity of natural filtrations
Time dependent subordination and Markov processes with jumps
Time reversal of non-Markov point processes
Time-substitution based on fluctuating additive functionals (Wiener-Hopf factorization for infinitesimal generators)
Transience and non-explosion of certain stochastic Newtonian systems.
Transitions on a noncompact Cantor set and random walks on its defining tree
First, noncompact Cantor sets along with their defining trees are introduced as a natural generalization of -adic numbers. Secondly we construct a class of jump processes on a noncompact Cantor set from given pairs of eigenvalues and measures. At the same time, we have concrete expressions of the associated jump kernels and transition densities. Then we construct intrinsic metrics on noncompact Cantor set to obtain estimates of transition densities and jump kernels under some regularity conditions...