Related papers: Stochastic equations generating continuous multipl…
In this paper we establish a mathematical framework which may be used to design Monte-Carlo simulations for a class of time irreversible dynamic systems, such as incompressible fluid flows, including turbulent flows in wall-bounded regions,…
Sequential Monte Carlo Samplers are a class of stochastic algorithms for Monte Carlo integral estimation w.r.t. probability distributions, which combine elements of Markov chain Monte Carlo methods and importance sampling/resampling…
This paper exposes a novel exploratory formalism, which end goal is the numerical simulation of the dynamics of a cloud of particles weakly or strongly coupled with a turbulent fluid. Giventhe large panel of expertise of the list of…
We consider a stochastic differential equation of the form \[dX_t=\theta a(t,X_t)\,dt+\sigma_1(t,X_t)\sigma_2(t,Y_t)\,dW_t\] with multiplicative stochastic volatility, where $Y$ is some adapted stochastic process. We prove…
After collecting data from observations or experiments, the next step is to build an appropriate mathematical or stochastic model to describe the data so that further studies can be done with the help of the models. In this article, the…
A stochastic dynamics $({\bf X}(t))_{t\ge0}$ of a classical continuous system is a stochastic process which takes values in the space $\Gamma$ of all locally finite subsets (configurations) in $\Bbb R$ and which has a Gibbs measure $\mu$ as…
Obtaining accurate field statistics continues to be one of the major challenges in turbulence theory and modeling. From the various existing modeling approaches, multifractal models have been successful in capturing intermittency in…
The smoothing distribution is the conditional distribution of the diffusion process in the space of trajectories given noisy observations made continuously in time. It is generally difficult to sample from this distribution. We use the…
Uncertainties are abundant in complex systems. Mathematical models for these systems thus contain random effects or noises. The models are often in the form of stochastic differential equations, with some parameters to be determined by…
We study the properties of solutions of stochastic differential equations driven by processes generating loops in free nilpotent groups. We are in particular interested in existence and smoothness for the density.
Stochastic Master equations or quantum filtering equations for mixed states are well known objects in quantum physics. Building a mathematically rigorous theory of these equations in infinite-dimensional spaces is a long standing open…
In this manuscript we give thought to the aftermath on the stable probability density function when standard multiplicative cascades are generalised cascades based on the $q$-product of Borges that emerged in the context of non-extensive…
We present limit theorems for a sequence of Piecewise Deterministic Markov Processes (PDMPs) taking values in a separable Hilbert space. This class of processes provides a rigorous framework for stochastic spatial models in which discrete…
We give an account of matter and (basically) a solution of a new class of problems synthesizing percolation theory and branching diffusion processes. They led us to realizing a novel type of stochastic processes, namely branching processes…
One of approaches to quantum gravity is different models of a discrete pregeometry. An example of a discrete pregeometry on a microscopic scale is introduced. This is the particular case of a causal set. The causal set is a locally finite…
Towards the end of the last century, B. Mandelbrot saw the importance, revealed the beauty, and robustly promoted (multi-)fractals. Multiplicative cascades are closely related and provide simple models for the study of turbulence and chaos.…
By using the matrix formulation of the two-step approach to distributions of patterns in random sequences, recurrence and explicit formulas for the generating functions of successions in random permutations of arbitrary multisets are…
Complex systems are often characterized by the interplay of multiple interconnected dynamical processes operating across a range of temporal scales. This phenomenon is widespread in both biological and artificial scenarios, making it…
Stochastic line integrals provide a useful tool for quantitatively characterizing irreversibility and detailed balance violation in noise-driven dynamical systems. A particular realization is the stochastic area, recently studied in coupled…
The martingale expansion provides a refined approximation to the marginal distributions of martingales beyond the normal approximation implied by the martingale central limit theorem. We develop a martingale expansion framework specifically…