Typos

Author: pmenczel

tutorials-v5/time-evolution/022_v5_paper-smesolve.md

@@ -5,7 +5,7 @@ jupyter:
       extension: .md
       format_name: markdown
       format_version: '1.3'
-      jupytext_version: 1.13.8
+      jupytext_version: 1.16.4
   kernelspec:
     display_name: Python 3 (ipykernel)
     language: python
@@ -27,7 +27,7 @@ However, this solver is of course quite general and can thus also be applied to
 In this example we look at an optical cavity whose output is subject to homodyne detection.
 Such a cavity obeys the general stochastic master equation
 
-$d \rho(t) = -i [H, \rho(t)] dt + \mathcal{D}[a] \rho (t) dt + \mathcal{H}[a] \rho dW(t)$
+$d \rho(t) = -i [H, \rho(t)] dt + \mathcal{D}[a] \rho (t) dt + \mathcal{H}[a] \rho\, dW(t)$
 
 with the Hamiltonian
 
@@ -41,7 +41,7 @@ The stochastic part
 
 $\mathcal{H}[a]\rho = a \rho + \rho a^\dagger - tr[a \rho + \rho a^\dagger]$
 
-captures the conditioning of the trajectory through continious monitoring of the operator $a$.
+captures the conditioning of the trajectory through continuous monitoring of the operator $a$.
 The term $dW(t)$ is the increment of a Wiener process that obeys $\mathbb{E}[dW] = 0$ and $\mathbb{E}[dW^2] = dt$.
 
 Note that a similiar example is available in the [QuTiP user guide](https://qutip.readthedocs.io/en/qutip-5.0.x/guide/dynamics/dynamics-stochastic.html#stochastic-master-equation).
@@ -72,7 +72,7 @@ mon_op = np.sqrt(kappa) * a  # continiously monitored operators
 
 ## Solving for the Time Evolution
 
-We calculate the predicted trajectory conditioned on the continious monitoring of operator $a$.
+We calculate the predicted trajectory conditioned on the continuous monitoring of the operator $a$.
 This is compared to the regular `mesolve()` solver for the same model but without resolving conditioned trajectories.
 
 ```python
@@ -96,7 +96,7 @@ stoc_solution = smesolve(
 
 We plot the averaged homodyne current $J_x = \langle x \rangle + dW / dt$ and the average system behaviour $\langle x \rangle$ for 500 trajectories.
 This is compared with the prediction of the regular `mesolve()` solver that does not include the conditioned trajectories.
-Since the conditioned expectation values do not depend on the trajectories, we expect that this reproduces the result of the standard `me_solve`.
+Since the conditioned expectation values do not depend on the trajectories, we expect that this reproduces the result of the standard `mesolve()`.
 
 ```python
 stoc_meas_mean = np.array(stoc_solution.measurement).mean(axis=0)[0, :].real