This work is devoted to the travelling wave solutions and asymptotic speed for a two-species stochastic competitive system driven by multiplicative Itô type white noise. By introduction of sup-solutions sub-solutions, existence approximations are proven under some conditions on parameters. Moreover, combining with Feynman-Kac formula, sub-solution, sup-solution, monotone iteration equilibria ki...

The application of the Feynman-Kac formula to Polaron models quantum theory leads path measure Brownian motion perturbed by a pair potential that is translation invariant both in space and time. An important problem this context validity central limit theorem infinite volume. We show existence relevant volume limits functional generality includes Frohlich polaron for all coupling constants. pro...

Adapting ideas of Daubechies and Klauder [J. Math. Phys. 26, 2239 (1985)] we derive a rigorous continuum path-integral formula for the semigroup generated by a spin Hamiltonian. More precisely, we use spin coherent vectors parametrized by complex numbers to relate the coherent representation of this semigroup to a suitable Schrödinger semigroup on the Hilbert space L2(R2) of Lebesgue square-int...

We study the quantization of the regularized hamiltonian, H , of the compactified D = 11 supermembrane with nontrivial winding. By showing that H is a relatively small perturbation of the bosonic hamiltonian, we construct a Dyson-type series for the heat kernel of H and prove its convergence in the topology of the von Neumann-Schatten classes so that e is ensured to be of finite trace. The resu...

In this paper, we give existence and uniqueness results for backward stochastic diierential equations when the generator has polynomial growth in the state variable. We deal with the case of xed terminal time as well as the case of random terminal time. The need for this type of extension of the classical existence and uniqueness results comes from the desire to provide a probabilistic represen...