Related papers: Stochastic Levy Differential Operators and Yang-Mi…
In this article we study the fractal Navier-Stokes equations by using stochastic Lagrangian particle path approach in Constantin and Iyer \cite{Co-Iy}. More precisely, a stochastic representation for the fractal Navier-Stokes equations is…
We prove that the stochastic differential equation $$ Y_{s,t}(x) = Y_{s,s}(x) + \int_0^{t-s} f(Y_{s,s+u}(x)) dX_{s+u}, Y_{s,s}(x)=x\in\R^d. $$ driven by a L\'evy process whose paths have finite p-variation almost surely for some $p\in[1,2)$…
The fractional material derivative appears as the fractional operator that governs the dynamics of the scaling limits of L\'evy walks - a stochastic process that originates from the famous continuous-time random walks. It is usually defined…
We consider the Dirac equation with an external Yang-Mills gauge field in a homogeneous space with an invariant metric. The Yang-Mills fields for which the motion group of the space serves as the symmetry group for the Dirac equation are…
We present an action for noncommutative supersymmetric Yang-Mills theory in ten-dimensions, and confirm its invariance under supersymmetry. We next add higher-order derivative terms to such a noncommutative supersymmetric action. These…
In enlarging the field content of pure Yang-Mills theory to a cutoff dependent matrix valued complex scalar field, we construct a vectorial operator, which is by definition invariant with respect to the gauge transformation of the…
We investigate Lie symmetries of the self-dual Yang-Mills equations in four-dimensional Euclidean space (SDYM). The first prolongation of the symmetry generating vector fields is written down, and its action on SDYM computed. Determining…
Mean-field stochastic differential equations, also called McKean--Vlasov equations, are the limiting equations of interacting particle systems with fully symmetric interaction potential. Such systems play an important role in a variety of…
In this paper approximation methods for infinite-dimensional Levy processes, also called (time-dependent) Levy fields, are introduced. For square integrable fields beyond the Gaussian case, it is no longer given that the one-dimensional…
In this article we consider parametric Bayesian inference for stochastic differential equations (SDE) driven by a pure-jump stable Levy process, which is observed at high frequency. In most cases of practical interest, the likelihood…
This paper concerns the numerical approximation for the invariant distribution of Markovian switching L\'evy-driven stochastic differential equations. By combining the tamed-adaptive Euler-Maruyama scheme with the Multi-level Monte Carlo…
We introduce the linear operators of fractional integration and fractional differentiation in the framework of the Riemann-Liouville fractional calculus. Particular attention is devoted to the technique of Laplace transforms for treating…
We consider the problem of the simulation of Levy-driven stochastic differential equations. It is generally impossible to simulate the increments of a Levy-process. Thus in addition to an Euler scheme, we have to simulate approximately…
We consider solutions of L\'evy-driven stochastic differential equations of the form $\mathrm{d} X_t=\sigma(X_{t-})\mathrm{d} L_t$, $X_0=x$ where the function $\sigma$ is twice continuously differentiable and maximal of linear growth and…
This work is devoted to deriving the Onsager-Machlup action functional for stochastic partial differential equations with (non-Gaussian) Levy process as well as Gaussian Brownian motion. This is achieved by applying the Girsanov…
In this article we introduce a finite difference approximation for integro-differential operators of L\'evy type. We approximate solutions of integro-differential equations, where the second order operator is allowed to degenerate. In the…
We establish the comparison principle and the existence of solutions of the integro-differential equations with L{\'e}vy operators. The L{\'e}vy operators of our interest are infinitesmal generator of the jump processes which could be…
We compute estimates for eigenvalues of a class of linear second-order elliptic differential operators in divergence form (with Dirichlet boundary condition) on a bounded domain in a complete Riemannian manifold. Our estimates are based…
Integrating out fast varying quantum fluctuations about Yang--Mills fields A_i and A_4, we arrive at the effective action for those fields at high temperatures. Assuming that the fields A_i and A_4 are slowly varying but that the amplitude…
L\'evy processes, known for their ability to model complex dynamics with skewness, heavy tails and discontinuities, play a critical role in stochastic modeling across various domains. However, inference for most L\'evy processes, whether in…