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In [6], the author characterized the extremal graph of bicyclic graphs with k pendant vertices with maximal signless Laplacian spectral radius2. For further details, we refer the
In this section we will apply the Young integral and rough path integral of local time defined in sections 2 and 3 to prove a useful extension to Itˆ o’s formula.. Assume the
Tevzadze , A Semimartingale Bellman equation and the variance- optimal martingale measure, Georgian Math. Tevzadze , A Semimartingale backward equation related to the p
We shall now investigate what happens with ρ, describing the evolution of the population forwards in time, when individual lineages mutate at constant rate µ. The heuristic
We prove that if the particle hopping rates of this process are in a particular relation with the densities of the initial measure then the distribution of this process at any time t
The case of Markov chains was first considered by Marton [20; 21] : for uniformly contracting Markov chains, in particular for ergodic Markov chains with finite state space,
We prove that a stochastic flow of reflected Brownian motions in a smooth multidimensional domain is differentiable with respect to its initial position.. The derivative is a linear
We also prove, under the same assumptions regarding the worldvolume at fixed time, that classical Nambu brackets on the worldvolume are quantised by the multibrackets corresponding
