In this work we propose an approximation scheme to transform a general stochastic hybrid system (SHS) into a SHS without forced transitions due to spatial guards. Such switching mechanisms are replaced by spontaneous transitions with state-dependent transition intensities (jump rates). The resulting switching diffusion process with random hybrid jumps is shown to converge in distribution to the...

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In this note, we establish $L^p$-bounds for the semigroup $e^{-tq^w(x,D)}$, $t \ge 0$, generated by a quadratic differential operator $q^w(x,D)$ on $\mathbb{R}^n$ that is Weyl quantization of complex-valued form $q$ defined phase space $\mathbb{R}^{2n}$ with non-negative real part $\operatorname{Re} q 0$ and trivial singular space. Specifically, show $e^{-tq^w(x,D)}$ bounded from $L^p(\mathbb{R...

The K-theory of a polynomial ring R[t] contains the K-theory of R as a summand. For R commutative and containing Q, we describe K∗(R[t])/K∗(R) in terms of Hochschild homology and the cohomology of Kähler differentials for the cdh topology. We use this to address Bass’ question, whether Kn(R) = Kn(R[t]) implies Kn(R) = Kn(R[t1, t2]). The answer to this question is affirmative when R is essential...

We investigate the persistence probability in the Voter model for dimensions d ≥ 2. This is achieved by mapping the Voter model onto a continuum reaction–diffusion system. Using path integral methods , we compute the persistence probability r(q, t), where q is the number of " opinions " in the original Voter model. We find r(q, t) ∼ exp[−f 2 (q)(ln t) 2 ] in d = 2; r(q, t) ∼ exp[−f d (q)t (d−2)...

and Applied Analysis 3 (1) V is continuous in ((n − 1)T, (n + τ − 1)T] × R + , ((n + τ − 1)T, nT] × R + and for each x ∈ R + , n ∈ N, lim (t,y)→ ((n+τ−1)T + ,x) V(t, y) = V((n + τ − 1)T + , x) and lim (t,y)→ (nT + ,x) V(t, y) = V(nT, x) exist. (2) V is locally Lipschitzian x. Definition 1. Letting V ∈ V 0 , one defines the upper right derivative of V with respect to the impulsive differential s...